Simplify Square Root of 89304

Here we will show you two methods that you can use to simplify the square root of 89304. In other words, we will show you how to find the square root of 89304 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√89304 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 89304 to simplify the square root of 89304. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 89304. The factors of 89304 are 1, 2, 3, 4, 6, 8, 12, 24, 61, 122, 183, 244, 366, 488, 732, 1464, 3721, 7442, 11163, 14884, 22326, 29768, 44652, and 89304. Furthermore, the greatest perfect square on this list is 14884 and the square root of 14884 is 122. Therefore, A equals 122.

B = Calculate 89304 divided by the greatest perfect square from the list of all factors of 89304. We determined above that the greatest perfect square from the list of all factors of 89304 is 14884. Furthermore, 89304 divided by 14884 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 89304 in its simplest radical form as follows:

√89304 = A√B

√89304 = 122√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 89304 to simplify the square root of 89304 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 89304 and then take the square root of that product. The prime factors that multiply together to make 89304 are 2 x 2 x 2 x 3 x 61 x 61. When we strip out the pairs only, we get 2 x 2 x 61 x 61 = 14884 and the square root of 14884 is 122. Therefore, A equals 122.

B = Divide 89304 by the number (A) squared. 122 squared is 14884 and 89304 divided by 14884 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 89304 in its simplest radical form as follows:

√89304 = A√B

√89304 = 122√6

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Simplify Square Root of 89305
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